12a
0886
(K12a
0886
)
A knot diagram
1
Linearized knot diagam
4 6 7 12 9 3 2 11 1 5 8 10
Solving Sequence
5,10 1,11
9 6 8 12 4 2 3 7
c
10
c
9
c
5
c
8
c
12
c
4
c
1
c
2
c
7
c
3
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.07214 × 10
121
u
41
− 1.29009 × 10
122
u
40
+ ··· + 1.79683 × 10
124
b − 2.09627 × 10
125
,
1.21110 × 10
125
u
41
− 3.08153 × 10
125
u
40
+ ··· + 3.67991 × 10
127
a − 5.44579 × 10
128
,
u
42
− 3u
41
+ ··· − 7680u + 2048i
I
u
2
= h−u
2
a + b − 1, −4u
32
a − 6u
31
a + ··· + a + 8, u
33
+ 2u
32
+ ··· − 2u − 1i
I
u
3
= hb − a − 1, a
2
+ a + 2, u − 1i
I
u
4
= hb − u, a − 1, u
2
+ 1i
I
v
1
= ha, b + 1, 32v
5
+ 16v
4
+ 16v
3
+ 4v
2
+ 2v + 1i
* 5 irreducible components of dim
C
= 0, with total 117 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h5.07 × 10
121
u
41
− 1.29 × 10
122
u
40
+ · · · + 1.80 × 10
124
b − 2.10 ×
10
125
, 1.21 × 10
125
u
41
− 3.08 × 10
125
u
40
+ · · · + 3.68 × 10
127
a − 5.45 ×
10
128
, u
42
− 3u
41
+ · · · − 7680u + 2048i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
1
=
−0.00329111u
41
+ 0.00837392u
40
+ ··· − 21.9426u + 14.7987
−0.00282282u
41
+ 0.00717978u
40
+ ··· − 18.7314u + 11.6665
a
11
=
1
u
2
a
9
=
−0.000468286u
41
+ 0.00119414u
40
+ ··· − 3.21121u + 3.13219
0.00274209u
41
− 0.00695770u
40
+ ··· + 18.0721u − 11.2349
a
6
=
0.000392195u
41
− 0.00107102u
40
+ ··· + 1.79714u − 2.03513
−0.00149906u
41
+ 0.00367622u
40
+ ··· − 10.2811u + 6.35866
a
8
=
−0.00329111u
41
+ 0.00837392u
40
+ ··· − 21.9426u + 14.7987
0.00208209u
41
− 0.00535290u
40
+ ··· + 13.9562u − 8.59570
a
12
=
−0.000468286u
41
+ 0.00119414u
40
+ ··· − 3.21121u + 3.13219
−0.00282282u
41
+ 0.00717978u
40
+ ··· − 18.7314u + 11.6665
a
4
=
−0.000392195u
41
+ 0.00107102u
40
+ ··· − 1.79714u + 2.03513
−0.00147930u
41
+ 0.00368763u
40
+ ··· − 10.2886u + 6.57486
a
2
=
−0.00305058u
41
+ 0.00802983u
40
+ ··· − 20.7780u + 15.1603
−0.00409737u
41
+ 0.0103081u
40
+ ··· − 27.3367u + 16.8188
a
3
=
−0.00676311u
41
+ 0.0172674u
40
+ ··· − 46.9837u + 30.8098
−0.00457559u
41
+ 0.0113420u
40
+ ··· − 32.3525u + 17.7346
a
7
=
−0.00676311u
41
+ 0.0172674u
40
+ ··· − 46.9837u + 30.8098
0.00331935u
41
− 0.00806990u
40
+ ··· + 22.9950u − 11.5457
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0230966u
41
+ 0.0573171u
40
+ ··· − 173.318u + 88.0642
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
− 10u
41
+ ··· − 11111u + 1504
c
2
, c
3
, c
6
u
42
− 2u
41
+ ··· + 7u − 4
c
4
, c
5
32(32u
42
+ 48u
41
+ ··· + 20u
2
+ 2)
c
7
u
42
− 2u
40
+ ··· + 1136u − 448
c
8
, c
9
, c
11
c
12
u
42
− 5u
41
+ ··· − u − 1
c
10
u
42
− 3u
41
+ ··· − 7680u + 2048
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
+ 14y
41
+ ··· + 62115215y + 2262016
c
2
, c
3
, c
6
y
42
− 38y
41
+ ··· − y + 16
c
4
, c
5
1024(1024y
42
− 1280y
41
+ ··· + 80y + 4)
c
7
y
42
− 4y
41
+ ··· − 2874624y + 200704
c
8
, c
9
, c
11
c
12
y
42
+ 17y
41
+ ··· + 9y + 1
c
10
y
42
− 9y
41
+ ··· − 69468160y + 4194304
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.314188 + 1.053170I
a = 0.027002 + 0.483467I
b = −0.594138 + 0.750449I
5.98291 − 1.19095I 10.40868 + 3.12372I
u = −0.314188 − 1.053170I
a = 0.027002 − 0.483467I
b = −0.594138 − 0.750449I
5.98291 + 1.19095I 10.40868 − 3.12372I
u = 0.820994 + 0.197858I
a = 0.95965 + 1.29956I
b = 0.291149 + 0.470080I
6.19589 − 3.49276I 6.51052 + 0.13763I
u = 0.820994 − 0.197858I
a = 0.95965 − 1.29956I
b = 0.291149 − 0.470080I
6.19589 + 3.49276I 6.51052 − 0.13763I
u = −0.577314 + 0.526253I
a = −0.108552 + 0.213642I
b = −1.121680 + 0.508475I
8.12984 − 3.40777I 9.67454 − 1.62361I
u = −0.577314 − 0.526253I
a = −0.108552 − 0.213642I
b = −1.121680 − 0.508475I
8.12984 + 3.40777I 9.67454 + 1.62361I
u = −0.991104 + 0.788632I
a = 0.430066 − 0.979780I
b = 0.048227 − 0.652088I
0.103272 + 0.890316I 7.21863 − 1.89711I
u = −0.991104 − 0.788632I
a = 0.430066 + 0.979780I
b = 0.048227 + 0.652088I
0.103272 − 0.890316I 7.21863 + 1.89711I
u = 0.650573 + 0.315344I
a = −0.150923 − 0.123948I
b = −1.306350 − 0.336680I
7.29715 − 5.25882I 4.50219 + 8.83294I
u = 0.650573 − 0.315344I
a = −0.150923 + 0.123948I
b = −1.306350 + 0.336680I
7.29715 + 5.25882I 4.50219 − 8.83294I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.375562 + 0.527351I
a = 0.695747 − 0.521764I
b = −0.077418 − 0.331511I
0.199443 + 0.975184I 4.03278 − 6.08768I
u = −0.375562 − 0.527351I
a = 0.695747 + 0.521764I
b = −0.077418 + 0.331511I
0.199443 − 0.975184I 4.03278 + 6.08768I
u = −1.354830 + 0.085427I
a = 0.20811 + 1.54932I
b = 0.374024 + 0.802773I
5.97161 + 6.59731I 7.43283 − 8.44870I
u = −1.354830 − 0.085427I
a = 0.20811 − 1.54932I
b = 0.374024 − 0.802773I
5.97161 − 6.59731I 7.43283 + 8.44870I
u = −0.570711 + 0.284785I
a = −0.119513 + 0.107746I
b = −1.237960 + 0.273860I
1.86047 + 2.11675I −0.90328 − 11.17612I
u = −0.570711 − 0.284785I
a = −0.119513 − 0.107746I
b = −1.237960 − 0.273860I
1.86047 − 2.11675I −0.90328 + 11.17612I
u = 0.442682 + 0.457127I
a = −0.050983 − 0.171060I
b = −1.041130 − 0.367914I
2.47985 + 1.01844I 7.66650 + 3.92369I
u = 0.442682 − 0.457127I
a = −0.050983 + 0.171060I
b = −1.041130 + 0.367914I
2.47985 − 1.01844I 7.66650 − 3.92369I
u = 0.522304
a = −0.110575
b = −1.24864
3.67439 −7.95490
u = 1.54341 + 0.23309I
a = 0.243734 + 1.309960I
b = 0.237641 + 0.802950I
−0.35149 + 3.39390I 0. − 8.80504I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.54341 − 0.23309I
a = 0.243734 − 1.309960I
b = 0.237641 − 0.802950I
−0.35149 − 3.39390I 0. + 8.80504I
u = 0.433072
a = 1.51195
b = 0.203807
2.70015 1.03960
u = −1.32959 + 0.84020I
a = −0.48736 + 1.45749I
b = 0.570490 + 1.221150I
2.85618 + 8.34848I 0
u = −1.32959 − 0.84020I
a = −0.48736 − 1.45749I
b = 0.570490 − 1.221150I
2.85618 − 8.34848I 0
u = 1.29599 + 0.93912I
a = −0.58004 − 1.38071I
b = 0.59672 − 1.32586I
0.1604 − 18.2186I 0. + 9.92364I
u = 1.29599 − 0.93912I
a = −0.58004 + 1.38071I
b = 0.59672 + 1.32586I
0.1604 + 18.2186I 0. − 9.92364I
u = −1.32065 + 0.93583I
a = −0.55241 + 1.37129I
b = 0.56978 + 1.31805I
−5.4682 + 14.4315I 0
u = −1.32065 − 0.93583I
a = −0.55241 − 1.37129I
b = 0.56978 − 1.31805I
−5.4682 − 14.4315I 0
u = 1.35470 + 0.90995I
a = −0.50581 − 1.37917I
b = 0.539500 − 1.285140I
−4.16980 − 10.14610I 0
u = 1.35470 − 0.90995I
a = −0.50581 + 1.37917I
b = 0.539500 + 1.285140I
−4.16980 + 10.14610I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.60722 + 1.63895I
a = −0.090576 − 0.705861I
b = −0.372413 − 1.065220I
2.41336 + 9.70431I 0
u = 0.60722 − 1.63895I
a = −0.090576 + 0.705861I
b = −0.372413 + 1.065220I
2.41336 − 9.70431I 0
u = 1.47227 + 0.94822I
a = −0.421850 − 1.297470I
b = 0.426915 − 1.286100I
−5.57375 − 10.06480I 0
u = 1.47227 − 0.94822I
a = −0.421850 + 1.297470I
b = 0.426915 + 1.286100I
−5.57375 + 10.06480I 0
u = −1.57270 + 0.94944I
a = −0.352961 + 1.267110I
b = 0.360707 + 1.251940I
−8.85361 + 5.99722I 0
u = −1.57270 − 0.94944I
a = −0.352961 − 1.267110I
b = 0.360707 − 1.251940I
−8.85361 − 5.99722I 0
u = −0.47063 + 1.78264I
a = −0.047981 + 0.738048I
b = −0.312174 + 1.017260I
−2.89576 − 5.73091I 0
u = −0.47063 − 1.78264I
a = −0.047981 − 0.738048I
b = −0.312174 − 1.017260I
−2.89576 + 5.73091I 0
u = 0.00561 + 1.91712I
a = 0.046167 − 0.779412I
b = −0.229375 − 0.915905I
−0.81742 + 1.38862I 0
u = 0.00561 − 1.91712I
a = 0.046167 + 0.779412I
b = −0.229375 + 0.915905I
−0.81742 − 1.38862I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.70614 + 0.93966I
a = −0.279714 − 1.240500I
b = 0.299896 − 1.205740I
−4.72570 − 1.89699I 0
u = 1.70614 − 0.93966I
a = −0.279714 + 1.240500I
b = 0.299896 + 1.205740I
−4.72570 + 1.89699I 0
9
II.
I
u
2
= h−u
2
a + b − 1, −4u
32
a − 6u
31
a + · · · + a + 8, u
33
+ 2u
32
+ · · · − 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
1
=
a
u
2
a + 1
a
11
=
1
u
2
a
9
=
4u
32
+ 6u
31
+ ··· − a − 2u
u
4
a − u
4
+ u
2
− 1
a
6
=
−2u
32
a + u
32
+ ··· + 4a − 4
−2u
32
− 4u
31
+ ··· + 9u + 4
a
8
=
4u
32
+ 6u
31
+ ··· − a − 1
−1
a
12
=
−u
2
a + a − 1
u
2
a + 1
a
4
=
−2u
32
a + 3u
32
+ ··· + 4a − 8
−2u
32
− 4u
31
+ ··· + 9u + 4
a
2
=
−4u
32
− 6u
31
+ ··· + 3a − 7
−u
12
a + u
12
+ ··· − 7u
2
+ 3
a
3
=
u
24
a − 5u
22
a + ··· + a − 8
u
26
a − 4u
24
a + ··· − 6u
2
+ 1
a
7
=
4u
32
+ 6u
31
+ ··· − a + 3
u
24
a − u
24
+ ··· + 6u
2
− 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
32
− 20u
30
− 4u
29
+ 72u
28
+ 16u
27
− 180u
26
− 56u
25
+ 360u
24
+ 128u
23
− 580u
22
−
248u
21
+ 772u
20
+ 384u
19
− 848u
18
− 500u
17
+ 760u
16
+ 548u
15
− 532u
14
− 496u
13
+
264u
12
+ 372u
11
− 52u
10
− 220u
9
− 48u
8
+ 92u
7
+ 56u
6
− 24u
5
− 28u
4
− 4u
3
+ 4u
2
+ 6
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
33
− 6u
32
+ ··· + 128u − 23)
2
c
2
, c
3
, c
6
(u
33
− 2u
32
+ ··· + u
2
+ 1)
2
c
4
, c
5
u
66
− u
65
+ ··· − 115818u + 36557
c
7
(u
33
+ 3u
32
+ ··· + 32u + 7)
2
c
8
, c
9
, c
11
c
12
u
66
+ 10u
65
+ ··· + 4u + 1
c
10
(u
33
+ 2u
32
+ ··· − 2u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
33
+ 14y
32
+ ··· − 2062y −529)
2
c
2
, c
3
, c
6
(y
33
− 30y
32
+ ··· − 2y −1)
2
c
4
, c
5
y
66
− 27y
65
+ ··· − 41121383020y + 1336414249
c
7
(y
33
− 3y
32
+ ··· + 394y −49)
2
c
8
, c
9
, c
11
c
12
y
66
+ 40y
65
+ ··· + 20y + 1
c
10
(y
33
− 10y
32
+ ··· − 2y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.014300 + 0.118417I
a = −0.596166 + 1.043440I
b = 0.645673 + 1.202080I
−6.89406 + 3.13953I −4.34254 − 5.36114I
u = −1.014300 + 0.118417I
a = −0.27011 − 1.48522I
b = 0.36912 − 1.44230I
−6.89406 + 3.13953I −4.34254 − 5.36114I
u = −1.014300 − 0.118417I
a = −0.596166 − 1.043440I
b = 0.645673 − 1.202080I
−6.89406 − 3.13953I −4.34254 + 5.36114I
u = −1.014300 − 0.118417I
a = −0.27011 + 1.48522I
b = 0.36912 + 1.44230I
−6.89406 − 3.13953I −4.34254 + 5.36114I
u = −0.877024 + 0.414488I
a = −0.765285 + 0.116859I
b = 0.627802 + 0.626194I
−0.262282 − 0.735872I 3.32687 − 0.76984I
u = −0.877024 + 0.414488I
a = 0.41594 − 1.75908I
b = −0.030432 − 1.353230I
−0.262282 − 0.735872I 3.32687 − 0.76984I
u = −0.877024 − 0.414488I
a = −0.765285 − 0.116859I
b = 0.627802 − 0.626194I
−0.262282 + 0.735872I 3.32687 + 0.76984I
u = −0.877024 − 0.414488I
a = 0.41594 + 1.75908I
b = −0.030432 + 1.353230I
−0.262282 + 0.735872I 3.32687 + 0.76984I
u = 1.039060 + 0.162429I
a = −0.558017 − 0.929889I
b = 0.726138 − 1.167780I
−1.75770 − 6.51294I 1.10617 + 5.98872I
u = 1.039060 + 0.162429I
a = −0.16397 + 1.48174I
b = 0.32713 + 1.50533I
−1.75770 − 6.51294I 1.10617 + 5.98872I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.039060 − 0.162429I
a = −0.558017 + 0.929889I
b = 0.726138 + 1.167780I
−1.75770 + 6.51294I 1.10617 − 5.98872I
u = 1.039060 − 0.162429I
a = −0.16397 − 1.48174I
b = 0.32713 − 1.50533I
−1.75770 + 6.51294I 1.10617 − 5.98872I
u = 0.705062 + 0.789522I
a = 0.921945 + 0.609371I
b = 0.205194 + 0.949502I
−0.79038 + 2.85888I 4.03469 − 3.31371I
u = 0.705062 + 0.789522I
a = 0.279153 + 1.164250I
b = −0.331425 + 0.163823I
−0.79038 + 2.85888I 4.03469 − 3.31371I
u = 0.705062 − 0.789522I
a = 0.921945 − 0.609371I
b = 0.205194 − 0.949502I
−0.79038 − 2.85888I 4.03469 + 3.31371I
u = 0.705062 − 0.789522I
a = 0.279153 − 1.164250I
b = −0.331425 − 0.163823I
−0.79038 − 2.85888I 4.03469 + 3.31371I
u = −0.752029 + 0.757937I
a = 0.361706 − 0.918628I
b = −0.050445 − 0.404144I
0.112103 + 0.911954I 6.34870 − 3.13722I
u = −0.752029 + 0.757937I
a = 0.652021 − 0.835679I
b = 0.041525 − 0.735838I
0.112103 + 0.911954I 6.34870 − 3.13722I
u = −0.752029 − 0.757937I
a = 0.361706 + 0.918628I
b = −0.050445 + 0.404144I
0.112103 − 0.911954I 6.34870 + 3.13722I
u = −0.752029 − 0.757937I
a = 0.652021 + 0.835679I
b = 0.041525 + 0.735838I
0.112103 − 0.911954I 6.34870 + 3.13722I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.930115
a = −0.65592 + 1.44435I
b = 0.432557 + 1.249530I
−5.02884 −0.712880
u = 0.930115
a = −0.65592 − 1.44435I
b = 0.432557 − 1.249530I
−5.02884 −0.712880
u = 0.906723 + 0.575511I
a = 0.56023 + 1.45906I
b = −0.247726 + 1.300990I
−4.48415 − 2.21654I −2.16344 + 2.48417I
u = 0.906723 + 0.575511I
a = −0.298340 + 0.110070I
b = 0.738659 − 0.257328I
−4.48415 − 2.21654I −2.16344 + 2.48417I
u = 0.906723 − 0.575511I
a = 0.56023 − 1.45906I
b = −0.247726 − 1.300990I
−4.48415 + 2.21654I −2.16344 − 2.48417I
u = 0.906723 − 0.575511I
a = −0.298340 − 0.110070I
b = 0.738659 + 0.257328I
−4.48415 + 2.21654I −2.16344 − 2.48417I
u = −0.703249 + 0.821130I
a = 0.928128 − 0.470465I
b = 0.289870 − 0.987370I
4.82578 − 6.26770I 8.18982 + 3.24511I
u = −0.703249 + 0.821130I
a = 0.334947 − 1.220330I
b = −0.469566 − 0.167548I
4.82578 − 6.26770I 8.18982 + 3.24511I
u = −0.703249 − 0.821130I
a = 0.928128 + 0.470465I
b = 0.289870 + 0.987370I
4.82578 + 6.26770I 8.18982 − 3.24511I
u = −0.703249 − 0.821130I
a = 0.334947 + 1.220330I
b = −0.469566 + 0.167548I
4.82578 + 6.26770I 8.18982 − 3.24511I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.789844 + 0.799846I
a = 0.487617 + 1.144040I
b = −0.453252 + 0.597917I
6.34781 − 3.04389I 9.82618 + 2.90426I
u = 0.789844 + 0.799846I
a = 0.532299 + 0.438608I
b = 0.437352 + 0.665590I
6.34781 − 3.04389I 9.82618 + 2.90426I
u = 0.789844 − 0.799846I
a = 0.487617 − 1.144040I
b = −0.453252 − 0.597917I
6.34781 + 3.04389I 9.82618 − 2.90426I
u = 0.789844 − 0.799846I
a = 0.532299 − 0.438608I
b = 0.437352 − 0.665590I
6.34781 + 3.04389I 9.82618 − 2.90426I
u = −0.963141 + 0.632636I
a = 0.50716 − 1.36612I
b = −0.397323 − 1.338550I
−1.26824 + 5.40417I 2.83191 − 6.21521I
u = −0.963141 + 0.632636I
a = −0.1053880 − 0.0161506I
b = 0.924735 + 0.119912I
−1.26824 + 5.40417I 2.83191 − 6.21521I
u = −0.963141 − 0.632636I
a = 0.50716 + 1.36612I
b = −0.397323 + 1.338550I
−1.26824 − 5.40417I 2.83191 + 6.21521I
u = −0.963141 − 0.632636I
a = −0.1053880 + 0.0161506I
b = 0.924735 − 0.119912I
−1.26824 − 5.40417I 2.83191 + 6.21521I
u = −0.600852 + 0.549903I
a = −0.86327 − 1.33884I
b = 0.064649 + 0.491972I
−0.353626 − 0.577287I 5.08869 + 0.00847I
u = −0.600852 + 0.549903I
a = 1.59685 − 1.66405I
b = −0.006019 − 1.152790I
−0.353626 − 0.577287I 5.08869 + 0.00847I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.600852 − 0.549903I
a = −0.86327 + 1.33884I
b = 0.064649 − 0.491972I
−0.353626 + 0.577287I 5.08869 − 0.00847I
u = −0.600852 − 0.549903I
a = 1.59685 + 1.66405I
b = −0.006019 + 1.152790I
−0.353626 + 0.577287I 5.08869 − 0.00847I
u = −0.965280 + 0.710510I
a = 0.510940 − 1.295900I
b = −0.559425 − 1.254120I
−0.54191 + 4.66940I 4.86326 − 2.61989I
u = −0.965280 + 0.710510I
a = 0.0753159 − 0.0333818I
b = 0.986366 − 0.117562I
−0.54191 + 4.66940I 4.86326 − 2.61989I
u = −0.965280 − 0.710510I
a = 0.510940 + 1.295900I
b = −0.559425 + 1.254120I
−0.54191 − 4.66940I 4.86326 + 2.61989I
u = −0.965280 − 0.710510I
a = 0.0753159 + 0.0333818I
b = 0.986366 + 0.117562I
−0.54191 − 4.66940I 4.86326 + 2.61989I
u = 0.950716 + 0.751979I
a = 0.514981 + 1.266800I
b = −0.637045 + 1.165010I
5.85251 − 2.78863I 8.90822 + 2.57820I
u = 0.950716 + 0.751979I
a = 0.171542 + 0.057779I
b = 0.975434 + 0.264829I
5.85251 − 2.78863I 8.90822 + 2.57820I
u = 0.950716 − 0.751979I
a = 0.514981 − 1.266800I
b = −0.637045 − 1.165010I
5.85251 + 2.78863I 8.90822 − 2.57820I
u = 0.950716 − 0.751979I
a = 0.171542 − 0.057779I
b = 0.975434 − 0.264829I
5.85251 + 2.78863I 8.90822 − 2.57820I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998168 + 0.717071I
a = 0.488348 + 1.291390I
b = −0.61319 + 1.32172I
−1.67944 − 8.54919I 2.18347 + 8.15424I
u = 0.998168 + 0.717071I
a = 0.0890290 − 0.0366137I
b = 1.095340 + 0.109793I
−1.67944 − 8.54919I 2.18347 + 8.15424I
u = 0.998168 − 0.717071I
a = 0.488348 − 1.291390I
b = −0.61319 − 1.32172I
−1.67944 + 8.54919I 2.18347 − 8.15424I
u = 0.998168 − 0.717071I
a = 0.0890290 + 0.0366137I
b = 1.095340 − 0.109793I
−1.67944 + 8.54919I 2.18347 − 8.15424I
u = −1.009690 + 0.731074I
a = 0.482190 − 1.282250I
b = −0.65913 − 1.33376I
3.89061 + 12.09090I 6.43573 − 8.11579I
u = −1.009690 + 0.731074I
a = 0.1161080 + 0.0594886I
b = 1.144140 − 0.142559I
3.89061 + 12.09090I 6.43573 − 8.11579I
u = −1.009690 − 0.731074I
a = 0.482190 + 1.282250I
b = −0.65913 + 1.33376I
3.89061 − 12.09090I 6.43573 + 8.11579I
u = −1.009690 − 0.731074I
a = 0.1161080 − 0.0594886I
b = 1.144140 + 0.142559I
3.89061 − 12.09090I 6.43573 + 8.11579I
u = −0.129012 + 0.620035I
a = 1.84776 − 3.41708I
b = −0.226286 + 0.961189I
1.97739 + 4.07711I 8.72201 − 3.88410I
u = −0.129012 + 0.620035I
a = 3.72482 + 1.42811I
b = −0.141514 − 1.121170I
1.97739 + 4.07711I 8.72201 − 3.88410I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.129012 − 0.620035I
a = 1.84776 + 3.41708I
b = −0.226286 − 0.961189I
1.97739 − 4.07711I 8.72201 + 3.88410I
u = −0.129012 − 0.620035I
a = 3.72482 − 1.42811I
b = −0.141514 + 1.121170I
1.97739 − 4.07711I 8.72201 + 3.88410I
u = 0.159946 + 0.484229I
a = 1.35528 + 5.45781I
b = −0.128533 − 0.930176I
−3.28246 − 1.28200I 3.99671 + 5.16805I
u = 0.159946 + 0.484229I
a = 5.82216 − 0.87708I
b = −0.080363 + 1.085080I
−3.28246 − 1.28200I 3.99671 + 5.16805I
u = 0.159946 − 0.484229I
a = 1.35528 − 5.45781I
b = −0.128533 + 0.930176I
−3.28246 + 1.28200I 3.99671 − 5.16805I
u = 0.159946 − 0.484229I
a = 5.82216 + 0.87708I
b = −0.080363 − 1.085080I
−3.28246 + 1.28200I 3.99671 − 5.16805I
19
III. I
u
3
= hb − a − 1, a
2
+ a + 2, u − 1i
(i) Arc colorings
a
5
=
0
1
a
10
=
1
0
a
1
=
a
a + 1
a
11
=
1
1
a
9
=
−1
a − 1
a
6
=
−1
a
a
8
=
−a − 1
−1
a
12
=
−1
a + 1
a
4
=
1
−a
a
2
=
a + 1
1
a
3
=
a
a + 1
a
7
=
−a − 1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
10
(u − 1)
2
c
2
, c
3
, c
4
c
5
, c
6
(u + 1)
2
c
7
u
2
c
8
, c
9
, c
11
c
12
u
2
+ u + 2
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
10
(y −1)
2
c
7
y
2
c
8
, c
9
, c
11
c
12
y
2
+ 3y + 4
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.50000 + 1.32288I
b = 0.50000 + 1.32288I
−4.93480 −2.00000
u = 1.00000
a = −0.50000 − 1.32288I
b = 0.50000 − 1.32288I
−4.93480 −2.00000
23
IV. I
u
4
= hb − u, a − 1, u
2
+ 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
1
=
1
u
a
11
=
1
−1
a
9
=
u + 1
−1
a
6
=
2
2u − 1
a
8
=
1
u − 1
a
12
=
−u + 1
u
a
4
=
2
2u − 1
a
2
=
−1
−u + 1
a
3
=
1
u
a
7
=
1
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
(u + 1)
2
c
4
u
2
+ 2u + 2
c
5
u
2
− 2u + 2
c
6
(u − 1)
2
c
7
u
2
c
8
, c
9
, c
10
c
11
, c
12
u
2
+ 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
6
(y −1)
2
c
4
, c
5
y
2
+ 4
c
7
y
2
c
8
, c
9
, c
10
c
11
, c
12
(y + 1)
2
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 1.00000
b = 1.000000I
−1.64493 0
u = − 1.000000I
a = 1.00000
b = − 1.000000I
−1.64493 0
27
V. I
v
1
= ha, b + 1, 32v
5
+ 16v
4
+ 16v
3
+ 4v
2
+ 2v + 1i
(i) Arc colorings
a
5
=
v
0
a
10
=
1
0
a
1
=
0
−1
a
11
=
1
0
a
9
=
1
1
a
6
=
2v
v
a
8
=
0
1
a
12
=
1
−1
a
4
=
2v
−v
a
2
=
4v
2
−2v
2
− 1
a
3
=
−16v
4
−8v
4
− 4v
2
− 1
a
7
=
−16v
4
8v
4
+ 4v
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 64v
4
+ 32v
3
+ 33v
2
+ 10
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
2
, c
3
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
4
32(32u
5
− 16u
4
+ 16u
3
− 4u
2
+ 2u − 1)
c
5
32(32u
5
+ 16u
4
+ 16u
3
+ 4u
2
+ 2u + 1)
c
6
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
7
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
8
, c
9
(u + 1)
5
c
10
u
5
c
11
, c
12
(u − 1)
5
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1
c
2
, c
3
, c
6
y
5
− 5y
4
+ 8y
3
− 3y
2
− y − 1
c
4
, c
5
1024(1024y
5
+ 768y
4
+ 256y
3
+ 16y
2
− 4y − 1)
c
7
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y − 1
c
8
, c
9
, c
11
c
12
(y − 1)
5
c
10
y
5
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.227849 + 0.600076I
a = 0
b = −1.00000
7.51750 + 4.40083I 8.62066 − 2.16111I
v = −0.227849 − 0.600076I
a = 0
b = −1.00000
7.51750 − 4.40083I 8.62066 + 2.16111I
v = 0.169555 + 0.411188I
a = 0
b = −1.00000
1.97403 − 1.53058I 2.78903 + 1.00704I
v = 0.169555 − 0.411188I
a = 0
b = −1.00000
1.97403 + 1.53058I 2.78903 − 1.00704I
v = −0.383413
a = 0
b = −1.00000
4.04602 14.4310
31
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u − 1)
2
(u + 1)
2
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)
· ((u
33
− 6u
32
+ ··· + 128u − 23)
2
)(u
42
− 10u
41
+ ··· − 11111u + 1504)
c
2
, c
3
((u + 1)
4
)(u
5
− u
4
+ ··· + u + 1)(u
33
− 2u
32
+ ··· + u
2
+ 1)
2
· (u
42
− 2u
41
+ ··· + 7u − 4)
c
4
1024(u + 1)
2
(u
2
+ 2u + 2)(32u
5
− 16u
4
+ 16u
3
− 4u
2
+ 2u − 1)
· (32u
42
+ 48u
41
+ ··· + 20u
2
+ 2)(u
66
− u
65
+ ··· − 115818u + 36557)
c
5
1024(u + 1)
2
(u
2
− 2u + 2)(32u
5
+ 16u
4
+ 16u
3
+ 4u
2
+ 2u + 1)
· (32u
42
+ 48u
41
+ ··· + 20u
2
+ 2)(u
66
− u
65
+ ··· − 115818u + 36557)
c
6
(u − 1)
2
(u + 1)
2
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)
· ((u
33
− 2u
32
+ ··· + u
2
+ 1)
2
)(u
42
− 2u
41
+ ··· + 7u − 4)
c
7
u
4
(u
5
− 3u
4
+ ··· − u + 1)(u
33
+ 3u
32
+ ··· + 32u + 7)
2
· (u
42
− 2u
40
+ ··· + 1136u − 448)
c
8
, c
9
((u + 1)
5
)(u
2
+ 1)(u
2
+ u + 2)(u
42
− 5u
41
+ ··· − u − 1)
· (u
66
+ 10u
65
+ ··· + 4u + 1)
c
10
u
5
(u − 1)
2
(u
2
+ 1)(u
33
+ 2u
32
+ ··· − 2u − 1)
2
· (u
42
− 3u
41
+ ··· − 7680u + 2048)
c
11
, c
12
((u − 1)
5
)(u
2
+ 1)(u
2
+ u + 2)(u
42
− 5u
41
+ ··· − u − 1)
· (u
66
+ 10u
65
+ ··· + 4u + 1)
32
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
4
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y − 1)
· (y
33
+ 14y
32
+ ··· − 2062y − 529)
2
· (y
42
+ 14y
41
+ ··· + 62115215y + 2262016)
c
2
, c
3
, c
6
((y − 1)
4
)(y
5
− 5y
4
+ ··· − y − 1)(y
33
− 30y
32
+ ··· − 2y − 1)
2
· (y
42
− 38y
41
+ ··· − y + 16)
c
4
, c
5
1048576(y − 1)
2
(y
2
+ 4)(1024y
5
+ 768y
4
+ ··· − 4y − 1)
· (1024y
42
− 1280y
41
+ ··· + 80y + 4)
· (y
66
− 27y
65
+ ··· − 41121383020y + 1336414249)
c
7
y
4
(y
5
− y
4
+ ··· + 3y − 1)(y
33
− 3y
32
+ ··· + 394y − 49)
2
· (y
42
− 4y
41
+ ··· − 2874624y + 200704)
c
8
, c
9
, c
11
c
12
((y − 1)
5
)(y + 1)
2
(y
2
+ 3y + 4)(y
42
+ 17y
41
+ ··· + 9y + 1)
· (y
66
+ 40y
65
+ ··· + 20y + 1)
c
10
y
5
(y − 1)
2
(y + 1)
2
(y
33
− 10y
32
+ ··· − 2y − 1)
2
· (y
42
− 9y
41
+ ··· − 69468160y + 4194304)
33
